Tape systems generally have two reels for storing tape, namely, a supply reel and a take-up reel, a capstan for moving the tape from reel to reel and tension arms for regulating the tape tension. High-performance tape systems also include servo systems, which regulate tape position and velocity. The servo systems rely on estimates of the tape pack radii to determine how to control the rotational speeds of the reels to achieve the desired tape velocity and position. The more accurate the estimates, the more precisely the servo system can control the movement of the tape.
Good estimates of the tape pack radii are fundamentally important in controlling all aspects of the system operations. For example, good estimates are important in determining from which reel to draw the tape to wrap around a scanner. An inaccurate estimate could result in an over-rotation of the selected reel. Further, good estimates are important to determining when to decelerate a high-speed rewind operation, again to avoid over-rotation of one of the reels that may result in the breaking of the tape of the detatchment of the tape from the reel. Also, good estimates are important to determine if there is sufficient tape available on the supply reel to complete a record operation. Inaccurate estimates of the reel pack radii can result in incomplete record operations, if the system sufficiently under estimates the tape position.
In prior known systems the tape pack radius is calculated from measurements of the angular positions of the reels and the capstan. The position measurements are made by, for example, optical encoders that count the number of slots that pass between a photo detector and a light source as the reel rotates. The calculations produce results that are at best as accurate as the position measurements, which tend to be "noisy." With optical encoders, for example, the measurement noise is due in large part to quantitization errors. At slow speeds these systems tend to produce relatively inaccurate results because the position measurements are comparable to the quantitization errors.
Certain prior systems have processed the noisy measurement using low-pass filters, in order to smooth them. However, this approach has two significant problems. First, the signals produced by these filters always lag behind the true tape pack radii, or in other words, the estimates are biased. Second, these filters are slow to converge. Moreover, there is an intrinsic tradeoff--the more the filter smooths the output signals, i.e., the estimates of the tape pack radii, the more lag is introduced into the system and the slower the convergence.